Enhancing information transfer from observations to unobserved state variables for mesoscale radar data assimilation

Transcription

1 Enhancing information transfer from observations to unobserved state variables for mesoscale radar data assimilation Weiguang Chang and Isztar Zawadzki Department of Atmospheric and Oceanic Sciences Faculty of Science, McGill University August, 014

2 Motivation In meso- and convective scales, radar data are almost the only high-resolution observations. Radar data contain radial velocity (one component of wind) and reflectivity (precipitation). Other variables cannot be observed. State variables in a NWP model are corrected by data assimilation in two procedures: 1. Updated through the analysis step. Correcting unobserved variables requires significant and reliable cross-covariances between errors of observed variable and unobserved variable. e.g.: Update temperature while assimilating radial velocity.. Modified by model integration. e.g.: After radial velocity is corrected, temperature is adusted gradually during model integration.

3 Motivation In meso- and convective scales, radar data are almost the only high-resolution observations. Radar data contain radial velocity (one component of wind) and reflectivity (precipitation). Other variables cannot be observed. State variables in a NWP model are corrected by data assimilation in two procedures: 1. Updated through the analysis step. Correcting unobserved variables requires significant and reliable cross-covariances between errors of observed variable and unobserved variable. e.g.: Update temperature while assimilating radial velocity.. Modified by model integration. e.g.: After radial velocity is corrected, temperature is adusted gradually during model integration.

4 Motivation Problem of radar data assimilation: In a real (not simulated observations) radar data assimilation system, the improvement brought by data analysis cannot last longer than ~3 hours. One possible reason: The unobserved variables (all model variables other than radial velocity and reflectivity), are difficult to be corrected. Any solution? This study tries to enhance the information transfer from observation to unobserved model variables. e.g.: in convective scale, vertical motion is important for triggering storms. But only a small component of the vertical motion can be observed by radar.

5 In order to efficiently correct the unobserved variables, the experiment is setup in the following manner. Ensemble Kalman Filter (EnKF) is used for data assimilation. EnKF can produce flow-dependent error cross-covariance. Environment Canada s Global Environmental Multiscale Limited Area Model (GEM-LAM) is applied in EnKF. Simulated phased-array radar observations are assimilated. Radar with phase-array technique has an array of antennas. The radar beam can be electronically steered by adusting the phases of these antennas. Such a radar is able to sample the atmosphere adaptively in space and time. Ensemble method Estimates the error statistics. Finds the locations where information is easier to be transferred. Phased-array technique Directs radar beam to scan sensitive areas.

6 Experiment Design NWP Model Experiment procedure A: LAM-15km B: LAM-.5km C: LAM-1km 80 members are generated from EC s operational global EnKF analysis. 300km by 300km extension. 1km horizontal grid spacing. 58 vertical levels until 10 hpa. Double-moment microphysics scheme. Vr is the only type of observation. Vertical motion (W) is the unobserved variable. Single step analysis is performed.

7 Experiment Design Simulated truth (model output around 800hPa) and simulated observations. Simulated true Vr field (m/s) Simulated true reflectivity (dbz) Simulated Vr obs (m/s) Simulated true W field (m/s)

8 Experiment Design Background error statistics (around 800hPa) calculated from 79 members. Std deviation of Vr error (m/s) Std deviation of W error (m/s) cross-correlation between Vr & W errors Ens. Mean of rain mixing ratio

9 The impact of Vr assimilation on W. How much improvement can W have by assimilating only radial velocity (Vr)? The reduction of error variance of W can be estimated from Kalman Filter Equation: f a f f f f 1 a f f X Μ ( X ) K var( X, HX )( ( HX, HX ) R) X X K( O HX ) var a f X Analysis Background Observation X O K Kalman Gain H Obs operator R Obs error covariance matrix index of ensemble member X contain only two elements: Vr and W. W W ( Vr, W ) 1 O Vr ( W is forecast error variance analysis error variance )

10 The impact of Vr assimilation on W. How much improvement can W have by assimilating only radial velocity (Vr)? The reduction of error variance of W can be estimated from Kalman Filter Equation: f a f f f f 1 a f f X Μ ( X ) K var( X, HX )( ( HX, HX ) R) X X K( O HX ) var a f X Analysis Background Observation X O K Kalman Gain H Obs operator R Obs error covariance matrix index of ensemble member X contain only two elements: Vr and W. W W ( Vr, W ) 1 O Vr ( W is forecast error variance analysis error variance ) Larger positive value indicates that W uncertainty can be more reduced. Contour shows the location of precipitation. In the northern areas, Vr observations are not able to correct W.

11 Observation strategies Observation strategy. Note: Values are calculated on model grids, not on radar coordinate. This is a rough estimation because spatial correlation and cross-correlation among other variables are not considered. There are 900 observations. Observations are chosen according to values from high to low. W Dark red shows the location of observations. Contour shows the location of precipitation.

12 Observation strategies 1st Strategy nd Strategy 3rd Strategy 900 observations are uniformly distributed everywhere in the domain. Traditional mechanical radar usually scans the entire atmosphere without preference. 900 observations are uniformly distributed only in the precipitation area. Radar with phase-array technique is able to skip some regions. 900 observations are distributed in order to reduce W uncertainty. Radar with phase-array technique can put more observations in particular areas as required by user. Generate simulated observations Assimilate them by EnKF for one time step Calculate the difference between background error and analysis error

13 Observation strategies 1st Strategy nd Strategy 3rd Strategy 900 observations are uniformly distributed everywhere in the domain. Traditional mechanical radar usually scans the entire atmosphere without preference. Reduction of W error standard deviation. 900 observations are uniformly distributed only in the precipitation area. Radar with phase-array technique is able to skip some regions. 900 observations are distributed in order to reduce W uncertainty. Radar with phase-array technique can put more observations in particular areas as required by user. 10 Generate simulated observations Assimilate them by EnKF for one time step Calculate the difference between background error and analysis error

14 Observation strategies 4th Strategy The W at present time can be improved by assimilating the Vr observations collected 5- min ago. Cross-cor. between W & Vr (5-min ago) Estimated W if obs. collected 5-min ago Blue contour: precipitation coverage at 5-min before. Orange points: Observation locations selected at 5-min before.

15 Quantitative analysis The figure shows the difference between total background error variance and total analysis error variance in percentage. Total variance is the sum of error variance at each grid point covered by precipitation calculated based on the ensemble mean. W (unobserved variable) uncertainty is more reduced when a more sophisticated strategy is used. Vr (observed variable) uncertainty is reduced more than W uncertainty.

16 Verification by the truth The quantitative analysis is based on the error variance calculated with respect to the ensemble mean. e.g. : W E ( W W ) When the truth is known, the error variance can also be calculated with respect to the truth. e.g. : W E ( W W ) t

17 Verification by the truth The quantitative analysis is based on the error variance calculated with respect to the ensemble mean. e.g. : W E ( W W ) When the truth is known, the error variance can also be calculated with respect to the truth. e.g. : W E ( W W ) t When the truth is used for evaluation, the improvement on W is much less. But a more sophisticated observation strategy is still able to reduce more uncertainty for W. The correction on Vr is more significant because Vr can be corrected directly in observation space.

18 Summary Ensemble method and phased-array radar technique are used in this study. Based on the background error statistics, an adaptive radar observation method is proposed in order to better improve the unobserved vertical motion by assimilating only radial velocity. This method put more observations at the locations where vertical motion is easier to be updated through cross-correlation between errors of W and Vr. The verification by the truth indicates that applying adaptive observation strategies on the analysis step of EnKF can reduce the uncertainty of unobserved W field, although the reduction is much smaller than the observed variable Vr.